Leeds United battled hard with Manchester United before succumbing, while a 2-1 defeat for Southampton against Wolves spelled the end for Nathan Jones.
Jurgen Klopp admitted his relief after Liverpool finally won their first Premier League game of 2023 with a 2-0 derby victory over Everton on Monday.
Mohamed Salah scored in the competition for the first time since Boxing Day and January signing Cody Gakpo notched his first goal for the club in the Anfield triumph.
Liverpool’s success ended a run of four league games without a win and lifted them to ninth in the table while struggling Everton remained in the bottom three.
Asked how he felt after the game, Liverpool manager Klopp said: “Relieved – that’s it, that’s the main feeling since the final whistle.
“I’m happy with the performance. It was necessary that we played the game we wanted to play and not the game Everton wanted to play."
Following the latest round of games, we have put together the best XI from the weekend’s action using ratings from WhoScored. Take a look...
1. 1. GoalkeeperDavid de Gea - 8.0
Manchester United's David de Gea clears from Leeds United's Crysencio Summerville during a clean sheet performance at Elland Road. (Picture: Bruce Rollinson) Photo: Bruce Rollinson
2. 2. Right-back Kenny Tete of Fulham - 7.6
Get this man in your Fantasy team - Kenny Tete of Fulham is tackled by Gustavo Scarpa of Nottingham Forest (Picture: Clive Rose/Getty Images) Photo: Clive Rose
3. 3. Left-back Pervis Estupinan of Brighton - 8.5
Pervis Estupinan of Brighton celebrates a goal which was then disallowed but it did not detract from a cracking performance at Palace. (Picture: Eddie Keogh/Getty Images) Photo: Eddie Keogh
4. 5. Left-centre-back Luke Shaw of Manchester United - 8.2
Luke Shaw, pictured clearing from Patrick Bamford, was deployed as a centre-back and left-back in this game, kept a clean sheet and made the decisive goal for Marcus Rashford (Picture: Bruce Rollinson) Photo: Bruce Rollinson